Question

How to prove $L_{2} ([0,1])$ $\cong$ $L_{2}(\mathbb{R})$

score 332 · Answer 1 · 2026-04-06 18:59:41

332

Views

How to prove $L_{2} ([0,1])$ $\cong$ $L_{2}(\mathbb{R})$

Published on 06 Apr 2026 - 18:59

score 230 · Answer 2 · 2026-04-08 09:08:35

230

Views

Is a function of a compact operator a compact operator?

Published on 08 Apr 2026 - 9:08

score 73 · Answer 3 · 2026-02-23 12:07:50

73

Views

Images of the functional calculi of an operator

Published on 23 Feb 2026 - 12:07

score 70 · Answer 4 · 2026-03-26 01:12:44

70

Views

Define the map $T(f)=a(x)f(x)$ where $a(x) \in C[-\pi,\pi]$ and $f \in L^2$, show that $T$ is not compact unless $a=0$

Published on 26 Mar 2026 - 1:12

score 105 · Answer 5 · 2026-03-26 01:28:42

105

Views

Continuously embedded subspace (with own topolog. structure) of a separable real Hilbert space is itself separable

Published on 26 Mar 2026 - 1:28

score 85 · Answer 6 · 2026-04-01 15:06:23

85

Views

Dirac Notation: How $|f\rangle= \sum_{j=1}^{\infty}|\phi_j\rangle\langle\phi_j|f\rangle$?

Published on 01 Apr 2026 - 15:06

score 402 · Answer 7 · 2026-03-27 07:48:26

402

Views

Projection onto a closed convex set in a general Hilbert space

Published on 27 Mar 2026 - 7:48

score 27 · Answer 8 · 2026-03-25 06:27:58

27

Views

Uniform approximation of derivatives in a separable Hilbert space

Published on 25 Mar 2026 - 6:27

score 148 · Answer 9 · 2020-07-07 12:22:26

148

Views

How to show that $(I+T/n)^{-1}$ converges strongly to the identity operator?

Published on 07 Jul 2020 - 12:22

score 1.3k · Answer 10 · 2026-03-30 07:00:22

1.3k

Views

Prove that the spectrum of a bounded, self-adjoint linear operator is real and non-negative iff the operator is positive

Published on 30 Mar 2026 - 7:00

score 76 · Answer 11 · 2020-07-08 06:10:09

76

Views

Inequality of a linear operator on Hilbert space.

Published on 08 Jul 2020 - 6:10

score 85 · Answer 12 · 2026-03-25 06:28:37

85

Views

Approximation of projection of a function and computation of dual basis

Published on 25 Mar 2026 - 6:28

score 58 · Answer 13 · 2020-07-08 15:13:03

58

Views

if $f$ is $C^1$ do we always have $\|f(y_n)-f(y)\|_{L^2(0,1)} \longrightarrow 0 ?$

Published on 08 Jul 2020 - 15:13

score 34 · Answer 14 · 2026-04-01 16:46:57

34

Views

Approximation by finite subsets and strong resolvent convergence

Published on 01 Apr 2026 - 16:46

score 122 · Answer 15 · 2026-02-23 01:05:17

122

Views

Identifying a generic Hilbert space $H$ with an $L^2$ space on some measure space.

Published on 23 Feb 2026 - 1:05

List Question

How to prove $L_{2} ([0,1])$ $\cong$ $L_{2}(\mathbb{R})$

Is a function of a compact operator a compact operator?

Images of the functional calculi of an operator

Define the map $T(f)=a(x)f(x)$ where $a(x) \in C[-\pi,\pi]$ and $f \in L^2$, show that $T$ is not compact unless $a=0$

Continuously embedded subspace (with own topolog. structure) of a separable real Hilbert space is itself separable

Dirac Notation: How $|f\rangle= \sum_{j=1}^{\infty}|\phi_j\rangle\langle\phi_j|f\rangle$?

Projection onto a closed convex set in a general Hilbert space

Uniform approximation of derivatives in a separable Hilbert space

How to show that $(I+T/n)^{-1}$ converges strongly to the identity operator?

Prove that the spectrum of a bounded, self-adjoint linear operator is real and non-negative iff the operator is positive

Inequality of a linear operator on Hilbert space.

Approximation of projection of a function and computation of dual basis

if $f$ is $C^1$ do we always have $\|f(y_n)-f(y)\|_{L^2(0,1)} \longrightarrow 0 ?$

Approximation by finite subsets and strong resolvent convergence

Identifying a generic Hilbert space $H$ with an $L^2$ space on some measure space.

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